modal analysis as a tool to resolve pump vibration issues · national standard (ansi)/hi 9.6.6...

Modal Analysis as a Tool to Resolve Pump Vibration Issues

John Koch

HDR, Bellevue, WA

[email protected]

ABSTRACT

Vibration spectrum analysis and modal analysis are tools designers and plant staff can use to

optimize their pumping systems. This paper specifically looks at the ways these sophisticated

tools were used to diagnose and solve operational and mechanical issues on a two-stage raw

sewage pumping station constructed in 1972 and upgrade twice since then to achieve its current

227 ML/d (60 mgd) design capacity.

The modal and vibration analysis resulted in solving an intermediate bearing support structure

issue, but uncovered other hydraulically induced vibration issues which will require additional

investigation and study to resolve.

KEYWORDS: Modal, vibration, Hydraulic Institute, pump, natural frequency, resonance

INTRODUCTION

The essential step in solving vibration problems is to understand resonance. High vibration

levels can be caused by resonance in the rotating elements of the pump shaft, impeller or the

motor rotor, in the structure of the pump and its volute, bearing housing or motor frame.

Severe vibration, more appropriately defined as vibration above the Hydraulic Institute Standard

(HI) recommended maximum limits as contained in ANSI/HI 9.6.4 can destroy bearings in

pumps and motors as well as destroy mechanical seals. Resonance conditions in mechanical

systems occur when the excitation forces coincide with the natural frequencies of the structure.

A key to defining the source of the resonance is to determine if the source of the resonance is in

the rotating elements of the pump or in the pump assembly including the pump base plate and

supports and the structure the pump and pump base are attached to. To identify a resonance

condition requires obtaining the operating vibration spectrums of the system and identifying the

natural frequencies of the system.

The rotating elements of a pump or motor can have a critical speed close to their operating

speed; however, no rotating element is ever intentionally designed to operate in its critical speed

or go through its critical speed. In my more than 45 years of commissioning equipment, there

has only been one instance where the rotating element was the source of excessive vibration and

that was a vertical pump’s motor shaft which was excited by the variable frequency drive (VFD)

carrier frequency. Figure 1 illustrates the excessive vibration of this installation. The vertical

axis is inches per second-root mean squared; the horizontal axis is frequency in Hz.

298Copyright© 2017 by the Water Environment Federation

WEF Collection Systems Conference 2017

Figure 1 – Motor Shaft Vibration

All other vibration issues that I have encountered have been attributed to excitation of the

pump/motor structure. Most often when a pump’s vibration exceeds HI limits, the issue is with

the pump and its base not with its shaft.

Almost all equipment in water and wastewater treatment plants are mounted on concrete

equipment pads with grout poured in and under the equipment base as illustrated in Photograph

1.



Photograph 1- Grouted Pump Base

Grouting the pump’s equipment base provides damping to the pump and motor. Damping

reduces the maximum amplitude of the vibration caused by resonance and in doing so can bring

the equipment into compliance with HI maximum vibration limits. This is one of the reasons to

make sure the equipment base is in full contact with the concrete equipment pad and all the air

bubbles are expelled from the pourable grout mixture.

The key tenet of resolving natural frequency issues is adding mass to a structure or stiffening the

structure to move the natural frequencies out of the operating range of the equipment. Adding

mass will typically lower the system’s natural frequency; whereas, stiffening the structure of a

rotating piece of equipment will raise its natural frequency. Photograph 2 illustrates where mass

was added to a pump in an attempt to lower its natural frequency below the pump’s operating

speed.



Photograph 2 – Mass Added to Pumps

Trying to do add mass and stiffen the structure most of the time is counterproductive. The

formula for calculating the reed critical frequency or natural frequency is:

Where k = stiffness and m = mass

Experimental modal analysis is based on measured frequency response functions between a force

applied to the structure and the response of the structure. The measured frequency response

functions are post processed using modal analysis software to identify the natural frequencies of

the structure. Accelerometers are used to measure the response of the structure and an

instrumented hammer is used to apply the force to the structure as shown in Photograph 3.

Added Weight



Photograph 3 – Impact Hammer to Determine Natural Frequency

The natural frequency of a system is a property of the system that is defined by the inertial and

elastic properties (mass and stiffness) of the structure. The inertial and elastic properties of a

structure are a function of the material properties and the geometry of the components of the

structure. Each natural frequency has a particular displacement pattern, called a mode shape, and

each mode shape is independent of all other mode shapes of the system.

To identify a resonance condition in pumping systems, the measured operating vibration

spectrums are used to identify high vibration levels at the natural frequencies obtained from the

modal analysis. The measured vibration spectrums are reviewed to identify any vibration levels

that exceed the maximum allowable levels as defined by accepted industry standards. For

components that have vibration levels above the maximum allowable levels, the vibration

spectrum is inspected to determine at which frequency(s) the high vibration levels reside. Once

the high vibration level frequency has been identified, it is compared to the results of the modal

analysis to determine if there is a resonance condition.



As important as the stiffness of the pump and structure to reduce vibration levels below a HI

maximum level is the hydraulic conditions at the inlet to the pump’s impeller. American

National Standard (ANSI)/HI 9.6.6 recommends a minimum of 5 diameters of unobstructed

straight pipe into a pump suction unless a long radius reducing elbow with more than 50% area

reduction is used. For a 300 mm (12-inch) pump suction this means a long radius 300 x 450 mm

(12 x 18-inch) elbow would be required.

Photograph 4 illustrates how dye in a standard radius elbow swirls into a pump inlet.

Photograph 4 – Standard Radius Elbow

Comparing the standard radius elbow to the long radius elbow in Photograph 5, the flow stream

is more uniform in the long radius reducing elbow than in the standard elbow. Turbulent flow

into the eye of the pump impeller will cause unstable flow conditions and potentially high

vibration levels in the pump.



Photograph 5 – Long Radius Reducing Elbow

BACKGROUND

A 227 ML/d (60 mgd) two-stage high head, greater that 76m (250 feet) total dynamic head

(TDH) raw sewage pumping station was evaluated for its problematic maintenance issues and

perceived vibration problems. Several studies and attempts to resolve the issues were performed

over the last 15 years including a hydraulic model study.

The station was configured with the discharge of the first pump routed to the intake of the second

stage pump. Photograph 6 illustrates the first and second stage pumps installed in the cramped

pump room.



Photograph 6 - Two Stage Pumping Units

Several of the maintenance issues in the pumping station were due to the tight quarters for

performing any maintenance related activities. Many of the operational problems with the

pumping units were the short suction piping and 90-degree fitting into the suction of these

vertically configured pumps. The three different levels for pumps and motors presented both

maintenance and operational issues with the units. Photograph 7 illustrates the motors on the

next level above the pump room level.



Photograph 7 - Pump Motor Level

The installation utilized a long shaft assembly between the two floors. The shafting is supported

by intermediate guide bearings approximately half way between the two floors which are

illustrated in Photograph 8.

Photograph 8 - Intermediate Guide Bearing Supports



Pumps and intermediate shaft bearings were typically rebuilt and replaced every 12-18 months

because of the failure of one or more of the components in each set of pumps.

METHODOLOGY

The initial vibration analysis for the two-stage raw sewage pumping station determined there

were vibration issues with the intermediate bearing assemblies which could be transmitting a

resonance vibration to the pumps below. The intermediate support bearing structure was a series

of parallel 41 cm (16-inch) wide flange beams (WF16X26) and 30 cm (12-inch) (C12x20.7)

cross support channel beams for each pump set as shown in Photograph 9.

Photograph 9 - Intermediate Bearing Supports

The multiple reference impact testing approach was used for this project where the response is

measured at fixed locations and the forces are applied at all of the locations used in the modal

analysis. Multiple reference impact testing is ideal for large structures like the intermediate

bearing structure because it simplifies the measurement process allowing the frequency response

functions to be acquired efficiently.



The intermediate bearing support frequency response function measurements were made using a

Dytran Instruments Model 5802A impulse hammer and 3 PCB Piezotronics Model 604B31 tri-

axial accelerometers. For each measurement point the structure was excited with the hammer

and 9 frequency response functions were measured. A total of 62 and 66 points were measured

on the stage 1 and stage 2 intermediate bearing support structures respectfully.

The measured frequency response functions were used to estimate the natural frequencies of the

intermediate bearing support structures. The OROS Modal 5.2 modal analysis software was

used to perform the modal analysis from the measured frequency response functions. For this

project, the OROS BroBand modal identification module was used which is based on the

Polyreference Least Squares Complex Frequency Algorithm.

The modal analysis identified four modes (natural frequencies) of interest in the 0-100 Hz

frequency range of the stage 1 and 2 intermediate bearing support structures. The operating

speeds of pump sets 1-4 were 1800 rpm (30 Hz) and pump sets 5-12 were 1200 rpm (20 Hz). The

modes of interest identified by modal analysis are shown in Table 1 and all are in or very close to

the pump operating ranges.

Table 1: Intermediate Bearing Support Natural Frequencies

Mode Stage 1 (Hz) Stage 2 (Hz)

1 17.08 19.38

2 19.09 21.71

3 20.97 30.60

4 29.15 33.86

The mode shape for the Stage 1 structure’s first natural frequency at 17.08 Hz is shown in Figure

2. The first mode is the center section of the intermediate bearing support which supports the

intermediate bearings for Pumps 5-8 deflecting in the Y (horizontal) direction.

Figure 2 - Stage 1 Mode Deflecting in the Y-Axis



The mode shape for the Stage 1 structure’s fourth natural frequency at 29.15 Hz is shown in

Figure 3. The 29.15 Hz mode shape in the Stage 1 intermediate bearing support is the structure

deflecting in the X (north-south) direction while bending in the Z direction (vertically) in a wave

fashion.

Figure 3 - Stage 1 Mode Deflecting in the X-Axis

Centrifugal pumps typically have two main sources of vibration as shown at rotating speed and

at blade pass frequency. Pumps 1-4 operate at 1,800 RPM (30 Hz) and the pump impellers have

2 blades with a blade pass frequency of 60 Hz. Pumps 5-12 operate at 1,200 RPM (20 Hz) and

the pump impellers have 3 blades with a blade pass frequency of 60 Hz. In Table 2, the first three

rows show the operating frequency and the first two harmonics for both pumps. The last three

rows in Table 2 show the blade pass frequency and its first two harmonics.

Table 2: Pump Operating and Blade Pass Frequencies (Hz)

Forcing Frequencies Pumps 1-4 Pumps 5-15

1X 30 20

2X 60 40

3X 90 60

1X Blade Pass 60 60

2X Blade Pass 120 120

3XBlade Pass 180 180

The maximum allowable vibration levels for the pumps, drive motors and intermediate bearing

support were determined using the Hydraulic Institute standard 9.6.4-2009, ISO 10816-3,

Technical Associates of Charlotte, P.C. criteria for overall condition rating and experience. The

maximum allowable vibration levels were set at 8.64 mm/sec (0.34 in/sec) root mean squared

(RMS) for the pumps, 5.08 mm/sec (0.20 in/sec) RMS for the intermediate bearing support, 4.57

mm/sec (0.18 in/sec) RMS for 74.6 kW(100 hp) drive motors and 7.11 mm/sec (0.28 in/sec)

RMS for the 298 to 373 kW (400 and 500 hp) drive motors.



All of the overall vibration levels measured on Pumps 1, 2, 5, 6, 9, and 10 were compared to the

maximum allowable. The results are shown in Table 3. The vibration levels, which exceed the

maximum allowable levels in Table 3, are red and the levels that are close to the maximum

allowable levels and warrant a closer look are highlighted in yellow.

Table 3 - Measured Overall Vibration Levels Pumps 1, 2, 5, 6, 9, and 10 mm/sec (in/sec)

RMS

Location Pump 1 Pump 2 Pump 5 Pump 6 Pump 9 Pump 10

Motor X 2.79

(0.11)

0.25

(0.01)

1.02

(0.04)

2.29

(0.09)

2.54

(0.10)

3.56

(0.14)

Motor Y 1.52

(0.06)

1.78

(0.07)

1.02

(0.04)

3.05

(0.12)

1.78

(0.07)

3.56

(0.14)

Motor Z 1.02

(0.04)

0.76

(0.03)

6.10

(0.24)

0.51

(0.02)

0.76

(0.03)

1.78

(0.07)

Intermediate Bearing X 7.37

(0.29)

2.79

(0.11)

2.79

(0.11)

1.52

(0.06)

2.03

(0.08) 5.84

(0.23)

Intermediate Bearing Y 1.52

(0.06) 4.06

(0.16)

4.83

(0.19)

3.05

(0.12) 21.59

(0.85)

16.26

(0.64)

Intermediate Bearing Z 1.02

(0.04)

1.52

(0.06)

2.03

(0.08) 4.32

(0.17)

1.52

(0.06)

2.79

(0.11)

Pump X 4.32

(0.17) 8.89

(0.35)

10.92

(0.43)

12.70

(0.50)

4.06

(0.16) 14.48

(0.57)

Pump Y 5.08

(0.20)

4.83

(0.19)

7.37

(0.29)

5.84

(0.23) 7.37

(0.29)

3.81

(0.15)

Pump Z 0.76

(0.03)

1.27

(0.05)

2.29

(0.09)

4.83

(0.19)

2.79

(0.11)

6.35

(0.25)

Pump 1 vibration levels are below the Hydraulic Institute maximum allowable levels at all

locations and directions, except the intermediate bearing X direction at 7.73 mm/sec (0.29 in/sec)

which is above the 5.10 mm/sec (0.20 in/sec) (RMS) maximum vibration level for the

intermediate bearing. Figure 4 shows the vibration spectrum from the Pump 1 intermediate

bearing. The dominant vibration level is at operating speed (30 Hz) of the pump. The modal

analysis also identified a natural frequency of the Stage 2 intermediate bearing support at 30.64

Hz. The mode shape for the Stage 2 intermediate bearing support at 30.64 Hz natural frequency

is predominately in the X direction. Based on these results, the high levels of vibration of the

Pump 1 intermediate bearing are due to a resonance condition.



Figure 4 - Pump 1 Intermediate Bearing Support Vibration Spectrum

Pump 2 vibration levels are below the Hydraulic Institute maximum allowable levels at all

locations and directions except the pump in the X direction. The vibration spectrum for Pump 2

shows that the X direction vibration is dominated by the blade pass frequency at 60 Hz and 2

times blade pass at 120 Hz as shown in Figure 5.

0 20 40 60 80 100 120 140 160 180 2000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Frequency (Hz)

Velo

city (

in/s

ec R

MS

)

Pump #1 Intermediate Bearing Support Vibration

X Direction

Y Direction

Z Direction



Figure 5 - Vibration Spectrum for Pump 2

The vibration at the blade pass and 2 times blade pass were below the maximum allowable

vibration level of 8.64 mm/sec (0.34 in/sec) RMS. Pump 2 does not have any natural

frequencies close to 60 Hz, which eliminates a resonance condition as the root cause of the high

vibration levels. Pump 2 also shows signs of cavitation, which is an indicator of hydraulic issues

with the pump, which will also increase the blade pass vibration levels. The cavitation induced

vibration in the 60-90 Hz range increased the overall vibration level to 8.89 mm/sec RMS (0.35

in/sec RMS).

The same analysis procedure was applied to Pumps 5-10 which, like Pumps 1 and 2, found the

vibration levels that exceeded the maximum allowable levels on the pumps were due to hydraulic

issues with the pumps and not due to resonance conditions in the pump structure. The high

vibration levels on the intermediate bearing support on Pumps 9 and 10 were due to resonance

conditions where the pump operating speed of 20 Hz was exciting the 20 Hz natural frequencies

in the intermediate bearing structure.

0 20 40 60 80 100 120 140 160 180 2000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Pump #2 Vibration

Frequency (Hz)

Velo

city (

in/s

ec R

MS

)

X Direction

Y Direction

Z Direction



RESULTS

The modal analysis suggested that stiffening the intermediate bearing support structure would

raise the reed critical speed of the supports. A finite element analysis was performed with the

data from the modal analysis which determined that welding a 7mm (1/4”) plate to the top and

bottom of the longitudinal beam structure would provide the necessary stiffness to change the

natural frequency of the support system. Photograph 10 shows the completed modifications to

the beams.

Photograph 10 - Modified Intermediate Bearing Support Structure

After the suggestions to stiffen the intermediate bearing structures were performed by the City,

another round of analysis of the entire pumping station was conducted to gather at one time the

following information to try and pinpoint the operational and maintenance issues with this

pumping station. The second round of vibration testing included:

Vibration signature of each pump, intermediate bearing and motor.

Flow from each two stage pump set measured with the stations flow meters that had been

recently calibrated.

Suction and discharge pressure from each pump measured with liquid filled calibrated

pressure gauges at the appropriate pressure ranges and fitted with diaphragm seals.

Power for each set of pumps measured at each motor starter.

The maximum allowable vibration levels were determined using the Hydraulic Institute standard

9.6.4-2009, ISO 10816-3, Technical Associates of Charlotte, P.C. criteria for overall condition

rating. The Hydraulic Institute Standard 9.6.4-2009 addresses the solids handling pump vibration

levels but does not address the motor or intermediate bearing. Technical Associates of Charlotte



criteria addresses vertical pump based on the height of the motor above grade but not a solids

handling pump specifically. Neither ISO 10816-3 nor Technical Associates of Charlotte

specifically address the intermediate bearing support maximum allowable vibration levels. The

maximum allowable vibration level for the intermediate bearing was determined from

experience.

Table 4 shows the maximum allowable vibration levels defined by the two (2) standards, (HI and

ISO) Technical Associates of Charlotte and experience. The last column on the right in the table

shows the maximum allowable vibration levels for this project based on the two (2) standards

and experience.

Table 4 - Maximum Allowable Vibration Levels (in/sec RMS)

Location HI 9.6.4-

2009 ISO 10816-3

Technical

Associates of

Charlotte

Criteria

used

Motor – 100 HP 0.18 0.18

Motor – 400 and 500 HP 0.28 0.28

Intermediate Bearing 0.20

Pump 0.34 0.39 0.34

Vibration measurements at the intermediate support structure were recorded after the

modifications were made by city personnel. The modifications had reduced the intermediate

bearing vibration levels from 22.00 mm/sec (0.86 in/sec) RMS to 3.60 mm/sec (0.14 in/sec)

RMS, considerably below the maximum allowable level of 5.00 mm/sec (0.2 in/sec) RMS. The

City had achieved success in reducing the resonance frequency and vibration issues associated

with the intermediate bearing support structure.

DISCUSSION

Vibration and modal analysis defined structural/mechanical issues with the two-stage vertical

end suction pumps. Structural issues were resolved with the intermediate bearing support

structure when the independent wide flanged beams were stiffened and modified to act as one

large box beam as shown in Photograph 10. With this piece of the puzzle resolved, the hydraulic

induced vibration issues can be further investigated.

The vibration signature of all of the pumps, once the resonance from the intermediate bearing

was reduced, was at blade pass and 2x blade pass frequency. Centrifugal pumps typically have a

dominant vibration at blade pass frequency.

Blade pass frequency is the number of impeller blades times the operating RPM. As an example

a two bladed impeller operating at 1800 RPM (30 Hz) would have a blade pass frequency at 60

Hz (30 Hz x 2). Issues that contribute to blade pass vibration are:

1. Non-laminar fluid flow to the pump suction and impeller.

2. Net suction positive pressure required (NPSH3) exceed net positive suction pressure

available (NPSHA). Or simply stated, the water level in the wet well is too low.



3. Pump operating outside of the pump’s preferred operating range (POR) and/or to the far

right of the acceptable operating range (AOR).

Further detailed investigation and analysis of the data collected will be required to pinpoint the

root cause of the continued hydraulic vibration issues with the raw sewage two-stage vertical end

suction centrifugal pumps.

CONCLUSION

Modal and vibration spectrum analysis, while not the ultimate resource for diagnosing and

resolving mechanical failures, are powerful tools to assist operation and maintenance personnel

in determining some of the root causes of equipment failure. As was the case in the investigation

of the two-stage vertical end suction pumps, one issue was eliminated; however, several other

potential problems were uncovered.

Vibration monitoring is a great evaluation tool that can be used to diagnose issues and problems.

It can and should be a tool for acceptance of installed pumps to confirm they meet the minimum

American National Standards Institute/Hydraulic Institute Standards.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the staff at the wastewater pumping stations for their

patience while all of the issues were investigated and satisfactorily resolved. I also wish to thank

the construction personnel that persevered during the issues with the suppliers and factory

personnel as well as the hydraulic modeling laboratory for their continued help in evaluating

pumping station hydraulics. Balancing Services Company and AVS Engineering, LLC are

thanked for their continued assistance in diagnosing vibration issues with rotating equipment

across the country.

REFERENCES

Hydraulic Institute (2009) Rotodynamic Pumps for Vibration Measurements and Allowable

Values; ANSI/HI 9.6.4; Parsippany, New Jersey.

Hydraulic Institute (2009) Rotodynamic Pumps for Pump Piping; ANSI/HI 9.6.6; Parsippany,

New Jersey.

Technical Associates of Charlotte, P.C. Vibration Criteria; Charlotte, North Carolina.

International Organization for Standardization, 10816-3:2009 – Mechanical Vibration, Geneva,

Switzerland



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